General Electric Co. is considering the sale of its train-signaling business to Alstom SA, in an effort to bolster the appeal of its $17 billion offer for the French engineering company's energy business and to counter German and Japanese suitors, according to people familiar with the matter.

Selling the signaling operations would help GE meet French President François Hollande's demand that the U.S. conglomerate help Alstom beef up...